Do simulated fishers dream of electric fish

Ernesto

25th April, 2018

Research Questions

  • To NGOs:
    • Flight simulator
  • To academics:
    • Heuristics zoo
  • To other ABM practitioners:
    • Contribute to general problems

Fisheries

  • Applied problem
  • Challenges:
    • Spatial
    • Feedbacks
    • Heterogeneity
    • Deep uncertainty
    • Individual-based data
  • Where social science goes to die

Where Social Science goes to die - part 1

  • Simplest possible fishery: \[ B_{t+1} = B_{t} + f(B_t) - C_t \]
  • For any \(C\) there is a \(B\) equilibrium
  • Fit by assuming every observation is an equilibrium
  • “Their use [equilibrium assumptions] in the past undoubtedly contributed to a number of major fishery collapses.” Haddon (2011)

Where Social Science goes to die - part 2

  • The profit maximizing boat; decides:
    • Where to fish
    • Optimal path
    • Number of trips per season
  • State space is immense:
    • Belief state of biomass available per fishing spot, per species, per time step
    • Location and action of all competitors
  • Bellman equation unsolvable

Metaphysical Dualism

  • What does computational tractability tells us about the real world?
  • “If your laptop can’t find it, then neither can the market.”

  • Pool player analogy
    • Church-Turing thesis

Two solutions in fisheries economics

  1. Ignore dynamics
    • Discrete choice models
    • Add indicators to correct for dynamics
    • “this is akin to postponing opening a gift in the knowledge that the joy of consumption will be greater for the wait” Baerenklau (2005)

Two solutions in fisheries economics

  1. Ignore fisheries:
    • Assume no space
    • Assume perfect knowledge
    • Assume fishing doesn’t kill of fish
    • Assume one boat

Pragmatism

  • Logbook data
  • Surveys
    • “I have only 5 spots and cycle through them”
    • “If in a bind, track highliner on radar and copy them”
    • “Explore a fixed proportion of tows”
    • “Draw peaks and valleys on maps”
  • Flexibility and Lucas critique

Zoo approach

  • Collect decision algorithms
    • From interviews
    • From CS-literature
  • Implement them in the same agent-based model
    • Test strengths/weaknesses in theory
    • Compare to real data
  • Use it for policy suggestions and sensitivity analysis

The One Agent Problem

The One Agent Problem

  • Find the most profitable spot to fish
  • Constraints:
    • No biomass information
    • No model knowledge
    • Environment changes over time
  • Subproblems:
    • How to explore
    • Explore-Exploit Tradeoff

Explore or Exploit ?

Explore or Exploit ?

Explore-Exploit

  • Stochastically choose to explore next trip with probability \(p\)
  • Explore in the neighborhood of where you currently go

One Agent world

One Agent sample run

Scaling issues

Scaling issues

Scaling issues

L’enfer, c’est les autres

  • Other boats consume biomass
  • You can use other boats information
  • How to imitate?
  • With probability \(p\) explore, otherwise copy somebody who’s doing better

Explore-Exploit-Imitate

Two Agents sample run

Many Agents

Cui prodest?

  • Model free
  • Adaptive

Oil Prices

Fish the Line (part 1)

Fish the Line (part 2)

Optimization

Gravitational Search - Demo

Kernel Regression

Kernel Regression - Demo

Which algorithm performs best in which scenarios?

Which algorithm performs best in which scenarios -pt 2

Which algorithm performs best in real scenarios

Estimating Models!

  • Complicated model depends on parameter vector \(\theta\)
  • All model estimation strategies do:
    1. Pick some summaries of data \(X\) \[ S = S_1(X), \dots, S_n(X) \]
    2. Generate similar summaries from model: \[ \hat S(\theta) = S_1(\theta),\dots, S_n(\theta) \]
    3. Minimize weighted distance: \[ \theta^* = \arg \min_{\theta} \left( S-\hat S (\theta) \right)^T W \left( S-\hat S (\theta) \right) \]
  • In economics one often assumes:
    • Ergodicity
    • 1 to 1 mapping
    • \(\Rightarrow\) consistency!

Issues

\[ \theta^* = \arg \min_{\theta} \left( S-\hat S (\theta) \right)^T W \left( S-\hat S (\theta) \right) \]

  • How to minimize?
    • ABC
    • BACCO (GP)
    • Simulated Annealing
  • Which summary statistics?
    • 4 to 1? (Altonji,Smith and Vidangos 2013)
    • Computational Costs? Collinearities?
  • Which weight?
    • In theory \(W \to \Omega^{-1}\)
    • In practice that is almost never better

Solution?

\[ \theta^* = \arg \min_{\theta} \left( S-\hat S (\theta) \right)^T W \left( S-\hat S (\theta) \right) \]

  • Just a complicated mapping \(S \to \theta\)
  • Discover it directly by regression
    • Run the model many times, for different \(\hat \theta\), generate \(\hat S(\theta)\)
    • Regress, possibly non-linearly (element-wise) $S $
    • Use regression directly to estimate parameters

RBC model example

RBC model results

variable average bias rmse predictivity
beta 0.9428448 0.0000170 0.0000024 0.9974501
delta 0.0250172 -0.0000283 0.0000003 0.8393244
eta 2.0025693 0.0004155 0.0014078 0.8924427
mu 0.2994697 0.0000126 0.0000357 0.8793255
sigma 0.0201519 -0.0000638 0.0000061 0.8100463
phi 0.9268363 0.0002791 0.0000242 0.9863231

RBC model example - cross-correlations

Cross-Correlations results

variable average bias rmse predictivity
beta 0.9442979 0.0003105 0.0000351 0.9635677
delta 0.0250639 -0.0000424 0.0000010 0.5021653
eta 2.0051800 -0.0008865 0.0063942 0.5070661
mu 0.3005239 0.0001406 0.0000819 0.7268164
sigma 0.0197322 -0.0000402 0.0000070 0.7954040
phi 0.9258460 -0.0001568 0.0001203 0.9265618

Advantages

  • Select summary statistics, weights and minimizes all at once
  • Output is understandable
  • Easy to test
  • Easy to add uncertainty about other parameters